How to use HTTP.GET in AngularJS correctly? In specific, for an external API call?

First, your success() handler just returns the data, but that’s not returned to the caller of getData() since it’s already in a callback. $http is an asynchronous call that returns a $promise, so you have to register a callback for when the data is available.

I’d recommend looking up Promises and the $q library in AngularJS since they’re the best way to pass around asynchronous calls between services.

For simplicity, here’s your same code re-written with a function callback provided by the calling controller:

var myApp = angular.module('myApp',[]);

myApp.service('dataService', function($http) {
    delete $http.defaults.headers.common['X-Requested-With'];
    this.getData = function(callbackFunc) {
        $http({
            method: 'GET',
            url: 'https://www.example.com/api/v1/page',
            params: 'limit=10, sort_by=created:desc',
            headers: {'Authorization': 'Token token=xxxxYYYYZzzz'}
        }).success(function(data){
            // With the data succesfully returned, call our callback
            callbackFunc(data);
        }).error(function(){
            alert("error");
        });
     }
});

myApp.controller('AngularJSCtrl', function($scope, dataService) {
    $scope.data = null;
    dataService.getData(function(dataResponse) {
        $scope.data = dataResponse;
    });
});

Now, $http actually already returns a $promise, so this can be re-written:

var myApp = angular.module('myApp',[]);

myApp.service('dataService', function($http) {
    delete $http.defaults.headers.common['X-Requested-With'];
    this.getData = function() {
        // $http() returns a $promise that we can add handlers with .then()
        return $http({
            method: 'GET',
            url: 'https://www.example.com/api/v1/page',
            params: 'limit=10, sort_by=created:desc',
            headers: {'Authorization': 'Token token=xxxxYYYYZzzz'}
         });
     }
});

myApp.controller('AngularJSCtrl', function($scope, dataService) {
    $scope.data = null;
    dataService.getData().then(function(dataResponse) {
        $scope.data = dataResponse;
    });
});

Finally, there’s better ways to configure the $http service to handle the headers for you using config() to setup the $httpProvider. Checkout the $http documentation for examples.